Model reduction of a high‐dimensional distributed parameter system (DPS) reduces the complexity of the system for various applications, from monitoring to model predictive control, while retaining its intrinsic properties. Unfortunately, the assumption of time–space separability usually fails to hold for popular time–space separation model reduction methods because the space and time of the DPS are inherently coupled. In this study, a time–space coupled learning method for a data‐driven model reduction of the DPS is presented. The proposed method has the advantage of preserving the time–space coupling characteristics and increasing the number of degrees of freedom during the model reduction learning process. A novel deep‐learning architecture is presented by combining encoder‐decoder networks with recurrent neural networks. Given a high‐dimensional system without an exact partial differential equation description, the dimension‐reduced model and its temporal dynamics are jointly learned using the collected input and output data. The learned model is then applied to predict the low‐dimensional representations and reconstruct the high‐dimensional outputs. The proposed method was demonstrated on the catalytic rod in a tubular reactor with recycle, the results of which indicate a better modeling accuracy and lower intrinsic dimensionality compared with classical time–space separation model reduction methods.

中文翻译：

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时空耦合学习方法的编解码器和RNN模型简化分布式参数系统

高维分布式参数系统（DPS）的模型简化可降低系统从监视到模型预测控制的各种应用的复杂性，同时保留其固有特性。不幸的是，时空可分离性的假设通常无法适用于流行的时空分离模型简化方法，因为DPS的时空是固有耦合的。在这项研究中，提出了一种时空耦合学习方法，用于减少DPS的数据驱动模型。所提出的方法的优点是在模型简化学习过程中保留了时空耦合特性并增加了自由度的数量。通过将编码器-解码器网络与递归神经网络相结合，提出了一种新颖的深度学习架构。对于没有精确的偏微分方程描述的高维系统，可以使用收集的输入和输出数据共同学习降维模型及其时间动态。然后将学习的模型应用于预测低维表示并重构高维输出。该方法在管式反应器的循环循环催化棒上得到了证明，与经典的时空分离模型还原方法相比，该方法的建模精度更高，固有维数更低。然后将学习的模型应用于预测低维表示并重构高维输出。该方法在管式反应器的循环循环催化棒上得到了证明，与经典的时空分离模型还原方法相比，该方法的建模精度更高，固有维数更低。然后将学习的模型应用于预测低维表示并重构高维输出。该方法在管式反应器的循环循环催化棒上得到了证明，与经典的时空分离模型还原方法相比，该方法的建模精度更高，固有维数更低。